It's mostly marketing, although in part clubs use it to distinguish among multiple teams within the same age group. Academy doesn't mean anything unless they are a USSDA club, in which case they usually use that designation rather than Academy. PDA is used to signify Pre-Development Academy, which could be significant in a USSDA club, but because it is for ages before Dev. Academy kicks in, it is quite loose. For example, several USSDA clubs have a PDA-I and PDA-II team, which basically means they have about 24 kids who are in the group of kids they are considering for Academy at U12. Problem is that if the PDA-II team is playing Flight II, for example, which I have seen, then that is probably an admission that the "PDA-II" designation means those kids aren't really being considered on par with the PDA-I kids and at most only a few of them would actually be candidates for Academy next year (and, in truth, those clubs could easily recruit an entirely new team for academy and the PDA designation only meant that they were the best of what they had at the time).
The colors like gold, black, white etc, are usually just the way clubs distinguish between teams at the age group and they represent the colors of the club uniforms. There are plenty of red, white, and blue teams too. A few clubs use the Coast Soccer League designation to identify the teams, in which case premier and silver actually mean something very specific. Otherwise, they are just names to indicate the order of their teams.
As for the directional add-ons, that is a function of club mergers that have made almost every team a surf, striker, FCGS, Pateadores, TFA etc. In many cases, if the team has a directional signal after their name, all bets are off about quality because they are really just a different club altogether from the mother ship.